Feigenbaum Constant

Robert P. Munafo, 2002 Dec 30.

A universal constant in mathematics (like pi=3.1415926... and
e=2.7182818...) that applies to nearly any parametrized iteration
function, such as that used for the Mandelbrot Set. It gives the limit
of the ratio between the parameter values at successive
period doubling bifurcations in a parameter space.

It is most easily seen as the ratio between the diameters of
successive mu-atoms in the sequence R2.1/2a, R2.1/2.1/2a,
R2.1/2.1/2.1/2a, ..., R2{.1/2}xNa, ... . The same ratio occurs in
all sequences of .1/2.1/2.1/2 mu-atoms that you find in the
Mandelbrot Set.

Keith Briggs has computed the value of the constant to very high
precision; here are the first 100 decimal places: